Name ________________________________________ Date __________________ Class__________________
LESSON
5-8
Reading Strategy
Use Vocabulary
You can solve radical equations in a three-step process. For example, to
solve the equation x  4  0 , follow the steps below.
STEP 1: Isolate
the radical
x 4
STEP 2: Raise
both sides to the
appropriate
power.
 x
2
  4
STEP 3: Simplify
and solve.
x  16
2
To isolate the radical means to have only
the radical on one side of the equation
and all other variables and constants on
the other side of the equation.
To understand what it means to raise a
number to a power, think about how the
exponent is located slightly higher than
the base.
Isolate the radical in each equation.
1.
x  3  0 _____________________________
2.
x  2  6  0 _____________________________
3. 4 x  8  0 _____________________________
4.
1
x  9  0 _____________________________
2
5. 2 x  6  4 _____________________________
To what power should both sides of each equation be raised?
6.
3
x  2 ________________
7.
8.
4
x  3  3 ________________
9.
x  2  1 ________________
3
x  4 ________________
Solve the following equations.
10.
x  7 1
11.
_________________________________________
x 2 3
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-66
Holt McDougal Algebra 2
7. x =
5
2
1
⎡
⎤
6. x 2 = ⎢( x + 6) 2 ⎥
⎣
⎦
8. x = 9; x = −2 is an extraneous solution.
9. −
5
≤x≤1
4
12. x > −21
13. x > 4
14. −2 ≤ x ≤ 123
15. v =
x2 = x + 6
x2 − x − 6 = 0
10. x ≥ 5
11. 7 ≤ x ≤ 16
(x − 3)(x + 2) = 0
x=3
Challenge
3
c
2
Reteach
1. 2x + 11 = 27
1. 15.25
2. 9
3. No solution
4. 19
5. 5
6. 3
7. 5 or −
2x = 16; x = 8
4 3 2(8) + 11 = 12
8. 8 or −1
10. 6
Problem Solving
1. Directly
x −3 =4
x − 3 = 16
2. a. d =
x = 19
s2
30f
b. About 58 ft
5 + 19 − 3 = 5
c. No; possible answer: his skid marks
were only 52 ft, not 58 ft.
5 + 16 = 5 + 4
d. About 33 mi/h
=99
3.
1
9
9. 7
4 3 36 = 12 9
2.
2
3. a. About 9 ft
x +4 =5
b. By at least 15 ft
x + 4 = 25
4. B
x = 21
5. A
Reading Strategies
2 21 + 4 =
2 25 = 2 ⋅ 5
= 10 9
4. 5x + 6 = 81
1.
x = −3
2.
x+2 =6
3.
x = −2
4.
x = 18
5.
x+6 =2
6. Third power
7. Second Power
5x = 75
9. Third power
x = 15
8. Fourth power
10. x = 64
11. x = 7
3
1
⎡
⎤
5. ⎢(6 x − 8) 3 ⎥ = 43
⎣
⎦
6x − 8 = 64
6x = 72
x = 12
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A67
Holt McDougal Algebra 2